Curriculum / Math / 6th Grade / Unit 3: Multi-Digit and Fraction Computation / Lesson 17
Math
Unit 3
6th Grade
Lesson 17 of 17
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Solve mathematical and real-world problems using the greatest common factor and least common multiple.
The core standards covered in this lesson
6.NS.B.4 — Find the greatest common factor of two whole numbers less than or equal to 100 and the least common multiple of two whole numbers less than or equal to 12. Use the distributive property to express a sum of two whole numbers 1—100 with a common factor as a multiple of a sum of two whole numbers with no common factor. For example, express 36 + 8 as 4 (9 + 2).
The foundational standards covered in this lesson
4.OA.B.4 — Find all factor pairs for a whole number in the range 1—100. Recognize that a whole number is a multiple of each of its factors. Determine whether a given whole number in the range 1—100 is a multiple of a given one-digit number. Determine whether a given whole number in the range 1—100 is prime or composite.
The essential concepts students need to demonstrate or understand to achieve the lesson objective
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Problems designed to teach key points of the lesson and guiding questions to help draw out student understanding
Two numbers can be described with the information below:
What are the two numbers?
Jason is preparing bundles of markers and pencils for a class activity. He wants to make the greatest number of bundles that he can, with the same number of markers and pencils in each bundle. Jason has 15 markers and 35 pencils. He writes the following equation to help him make sense of his supplies:
$${15+35=5(3+7)}$$
a. What does Jason’s equation tell him about how many bundles he can make and how many markers and pencils are in each bundle?
b. Mai, in another class, is also preparing bundles of markers and pencils. She has 24 markers and 36 pencils. She writes an equation and determines that she can make at most 4 bundles. Do you agree with Mai’s reasoning? Explain.
$${24+36=4(6+9)}$$
c. If you have 18 markers and 48 pencils, what is the greatest number of bundles you can make? How many markers and pencils in each bundle? Write an equation to represent this.
The florist can order roses in bunches of one dozen and lilies in bunches of 8. Last month she ordered the same number of roses as lilies. If she ordered no more than 100 roses, how many bunches of each could she have ordered? What is the smallest number of bunches of each that she could have ordered? Explain your reasoning.
The Florist Shop, accessed on Sept. 28, 2017, 4:42 p.m., is licensed by Illustrative Mathematics under either the CC BY 4.0 or CC BY-NC-SA 4.0. For further information, contact Illustrative Mathematics.
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A task that represents the peak thinking of the lesson - mastery will indicate whether or not objective was achieved
Two numbers less than 25 have a least common multiple of 60 and a greatest common factor of 5. What are the two numbers?
Find the greatest common factor of the two numbers below and rewrite the sum using the distributive property.
$${20 + 36}$$
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Lesson 16
Topic A: Dividing with Fractions
Interpret division problems as the number of items in each group or the number of groups of a given number of items. Write corresponding multiplication and division problems.
6.NS.A.1
Divide a fraction by a whole number using visual models and related multiplication problems.
Divide a whole number by a fraction using visual models.
Use visual models and patterns to develop a general rule to divide with fractions.
Solve and write story problems involving division with fractions.
Solve problems involving division with fractions.
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Topic B: Computing with Decimals
Add and subtract decimals using the standard algorithm.
6.NS.B.3
Multiply decimals using strategies, and develop an understanding of the standard algorithm.
Multiply decimals using the standard algorithm.
Divide multi-digit whole numbers using the standard algorithm.
6.NS.B.2
Divide numbers with decimal quotients. Divide decimals by whole numbers.
6.NS.B.2 6.NS.B.3
Divide decimals by decimals using the standard algorithm.
Solve problems involving decimals using all four operations.
Topic C: Applying the Greatest Common Factor and the Least Common Multiple
Use prime factorization to represent numbers as products of prime factors.
6.NS.B.4
Find the greatest common factor of two numbers. Solve application problems using the greatest common factor.
Find the least common multiple of two numbers. Solve application problems using the least common multiple.
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